Question

Find the equation of a line passing through the point (2, −5) and making an intercept of −3 on the Y-axis.

Answer 1

Given values:

• Point: (2, −5)
• Y-intercept (c): −3 (This means the line passes through the point (0, −3)

Using the slope formula with points (2, −5) and (0, −3):

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (-3 - (-5))/(0 - 2)`

`m = 2/-2`

∴ m = −1

Using the slope-intercept form y = mx + c:

y = −1x + (−3)

y = −x − 3

Rearranging into the standard form (Ax + By + C = 0):

x + y + 3 = 0

Hence, the equation of a line passing through the points is x + y + 3 = 0.